Win2K Pro is the user (client) version of Win2K Server.
Win2K Server allows a person to create web, mail, file, and gaming servers. This is NOT recommended as a day-to-day normal OS to diddle around on, unless you're trying to figure out how to run a server.
I have no clue what ADVACEDE Server is, but google is awesome for questions like these.
Windows 2000 is the desktop version of the operating system, geared to have hooks into all sorts of media and the like.
The server products are designed for network and storage performance. You do not want to use a server product for day-to-day workstation activities. The code is different enough that it could cause you problems.
Advanced server is geared to work with more memory and utilize multiple processors.